Algebraic multigrid for higher-order finite elements

  • Authors:

  • J. J. Heys;T. A. Manteuffel;S. F. McCormick;L. N. Olson

  • Affiliations:

  • Chemical and Materials Engineering Department, Arizona State University, Tempe, AZ 85287-6006, USA;Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA;Department of Applied Mathematics, University of Colorado at Boulder, Boulder, CO 80309, USA;Division of Applied Mathematics, Brown University, USA

  • Venue:
  • Journal of Computational Physics
  • Year:
  • 2005

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Abstract

Two related approaches for solving linear systems that arise from a higher-order finite element discretization of elliptic partial differential equations are described. The first approach explores direct application of an algebraic-based multigrid method (AMG) to iteratively solve the linear systems that result from higher-order discretizations. While the choice of basis used on the discretization has a significant impact on the performance of the solver, results indicate that AMG is capable of solving operators from both Poisson's equation and a first-order system least-squares (FOSLS) formulation of Stoke's equation in a scalable manner, nearly independent of basis order, p, for 3